Taylor Series Approximation for Cosine

For the following code to solve the taylor series approximation for cosine, I'm not getting the expected value for pi/2. Nor is the convergence flag ever getting to the desired value, which seems odd. I can successfully get values (expected) for pi/4 and pi- but pi/2 is all over the place. Is anyone able to see where I went wrong?

function [approxValue, diff, convFlag] = taylorEst(x, actualCos)
    % Finds the approximate value of cos(x). Solves until error is less than
    % 1e-4. The series for cosine is only has even powers, thus the 'n'
    % variable advancing by 2 each iteration. Returns the series
    % approximation and error between 'true' and 'estimated' values of
    % cosine.
    
    approxValue = 1; %initial value for series approximation
    n = 2; %Starts at 2 due to even power for cosine series
    k = 1; %number of terms
    diff = 1; %initial difference value
    relError = 1e-8; % Required relative error
    myrel = 1; %initial value for error
    
    %Solve the series approximation until difference between Matlab's
    %internal cos(x) and calculated cos(x) is less than 1e-4 or 20 iterations occur.

    while diff > .0001 && (k < 20)
        k = k + 1;
        oldVal = approxValue;
        approxValue = approxValue + ((-1) .^ (k-1) .* x .^ n) ./ factorial(n);
        diff = abs(actualCos - approxValue); %Compare true to approx value
        n = n + 2;  %Only applies positive powers for cosine series
        myrel = abs(((approxValue - oldVal) / approxValue));
    end
    
    disp(myrel)
    disp(relError)
    
    %Determine if the process has converged
    if myrel <= relError
        convFlag = 1;
    else
        convFlag = 0;
    end
end

[Vladimir Sovkov]

The expected value for pi/2 is zero, and your code produces 2.47372763646945e-05, which is quite well within your declared precision of .0001, so the result looks correct; decrease the desired precision and increase the number of terms in the series to get the smaller result. The problem with the convergence flag is because myrel = abs(((approxValue - oldVal) / approxValue)) is 1 wherenever oldVal=0, with any non-zero approxValue (with approxValue=0 as well, it is NaN).

[David Meixell]

Regarding the convergence flag, oldVal never equals zero, right? It's immediately initialized as 'oldVal = approxValue' and approxValue = 1, so myrel is never 1 and dividing by zero should never be encountered- unless I'm totally missing something.

[John D'Errico]

Really? So approxvalue NEVER changes? It is ALWAYS 1? I am so surprised. What then is the purpose of thise line?

approxValue = approxValue + ((-1) .^ (k-1) .* x .^ n) ./ factorial(n);

Admittedly, it will be exceedingly rare for that value to ever be zero, only for example at x=pi/2 would that be possible.